Time-dependent treatment of vibrational predissociation within the golden rule approximation

The time-dependent formulation for vibrational predissociation of weakly bound complexes within the golden rule treatment is presented. The quantum wave packet propagation in this formulation eliminates the difficulty of strenuous long time propagation of the full wave function due to long-lived resonance which occurs in the more exact time-dependent treatment. As a result, the new time-dependent treatment of vibrational predissociation essentially parallels that of direct photodissociation and therefore requires only short time propagation of the wave function. The wave packet propagation is efficiently carried out in the interaction picture and numerical calculations of rotational state distributions and the total decay width are presented for vibrational predissociation of HeCl₂. Correct rotational state distribution can be obtained with only a few time propagation steps owing to the use of large step size allowed in the interaction picture. Our approach provides an efficient method for the calculation of vibrational predissociation for more complex systems such as those with more than three atoms.